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math.APAug 1, 2010
17
citations (OpenAlex)
authors
  • Michael Herrmann
  • Barbara Niethammer
institutions
  • University of Oxford
arXiv abstractPDF
paper

Kramers' formula for chemical reactions in the context of Wasserstein gradient flows

arXiv:1008.3658 · doi:10.4310/CMS.2011.v9.n2.a15

Abstract

We derive Kramers' formula as singular limit of the Fokker-Planck equation with double-well potential. The convergence proof is based on the Rayleigh principle of the underlying Wasserstein gradient structure and complements a recent result by Peletier, Savaré and Veneroni.

revised proofs, 12 pages, 1 figure

Cited by in corpus (10)

  • Kramers' law: Validity, derivations and generalisations
  • Passing to the Limit in a Wasserstein Gradient Flow: From Diffusion to Reaction
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  • New porous medium Poisson-Nernst-Planck equations for strongly oscillating electric potentials
  • Cosh gradient systems and tilting
  • Rate-independent dynamics and Kramers-type phase transitions in nonlocal Fokker-Planck equations with dynamical control
  • A semiclassical approach to the Kramers--Smoluchowski equation
  • Asymptotics for scaled Kramers-Smoluchowski equations in several dimensions with general potentials
  • Mass transport in Fokker-Planck equations with tilted periodic potential
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